// 代码索引 5-1-1-1
#include <Eigen/Sparse>
#include <vector>
#include <QImage>

typedef Eigen::SparseMatrix<double> SpMat; // declares a column-major sparse matrix type of double
typedef Eigen::Triplet<double> T;

void insertCoefficient(int id, int i, int j, double w, std::vector<T> &coeffs,
                       Eigen::VectorXd &b, const Eigen::VectorXd &boundary)
{
    int n = int(boundary.size());
    int id1 = i + j * n;

    if (i == -1 || i == n)
        b(id) -= w * boundary(j); // constrained coefficient
    else if (j == -1 || j == n)
        b(id) -= w * boundary(i); // constrained coefficient
    else
        coeffs.push_back(T(id, id1, w)); // unknown coefficient
}

void buildProblem(std::vector<T> &coefficients, Eigen::VectorXd &b, int n)
{
    b.setZero();
    Eigen::ArrayXd boundary = Eigen::ArrayXd::LinSpaced(n, 0, M_PI).sin().pow(2);
    for (int j = 0; j < n; ++j)
    {
        for (int i = 0; i < n; ++i)
        {
            int id = i + j * n;
            insertCoefficient(id, i - 1, j, -1, coefficients, b, boundary);
            insertCoefficient(id, i + 1, j, -1, coefficients, b, boundary);
            insertCoefficient(id, i, j - 1, -1, coefficients, b, boundary);
            insertCoefficient(id, i, j + 1, -1, coefficients, b, boundary);
            insertCoefficient(id, i, j, 4, coefficients, b, boundary);
        }
    }
}

void saveAsBitmap(const Eigen::VectorXd &x, int n, const char *filename)
{
    Eigen::Array<unsigned char, Eigen::Dynamic, Eigen::Dynamic> bits = (x * 255).cast<unsigned char>();
    QImage img(bits.data(), n, n, QImage::Format_Indexed8);
    img.setColorCount(256);
    for (int i = 0; i < 256; i++)
        img.setColor(i, qRgb(i, i, i));
    img.save(filename);
}